Matrix Algebra: Theory, Computations, and Applications in Statistics

Matrix Algebra: Theory, Computations, and Applications in Statistics

Springer; 1 edition (July 27, 2007) | ISBN:0387708723 | 530 pages | PDF | 14 Mb

Matrix calculus is one of the most important areas of mathematics for facts analysis and for statistical theory. The first part of this main division presents the relevant aspects of the theory of matrix algebra with regard to >applications in statistics. This part begins with the fundamental concepts of vectors and vector spaces, nearest covers the basic algebraic properties of matrices, then describes the solvent properties of vectors and matrices in the multivariate calculus, and in conclusion discusses operations on matrices in solutions of linear systems and in eigenanalysis. This division is essentially self-contained. The second part of the book begins by a consideration of various types of matrices encountered in statistics, similar as projection matrices and positive definite matrices, and describes the uncommon properties of those matrices. The second part also describes some of the people applications of matrix theory in statistics, including linear models, multivariate analysis, and stochastic processes. The brief coverage in this part illustrates the matrix rationale developed in the first part of the book. The first two parts of the book can be used as the text by reason of a course in matrix algebra for statistics students, or as a supplemental text for various courses in linear models or multivariate statistics. The third part of this book covers numerical linear algebra. It begins by a discussion of the basics of numerical computations, and then describes just and efficient algorithms for factoring matrices, solving linear systems of equations, and extracting eigenvalues and eigenvectors. Although the volume is not tied to any particular software system, it describes and gives examples of the employment of modern computer software for numerical linear algebra. This part is essentially self-contained, though it assumes some ability to program in Fortran or C and/or the endowment to use R/S-Plus or Matlab. This part of the part can be used as the text for a course in statistical computing, or in the same proportion that a supplementary text for various courses that emphasize computations.

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